Particle Filters

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Particle Filters Monte Carlo Localization

• CS 3630 Intro to Perception and Robotics
• April 4, 2006
• Frank Dellaert Grant Schindler

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Probability of Robot Location
P(Robot Location)
Y
State space 2D, infinite states
X
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Sampling as Representation
P(Robot Location)
Y
X
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3D Particle filter for robot poseMonte Carlo
Localization

• Dellaert, Fox Thrun ICRA 99

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Sampling Advantages

• Arbitrary densities
• Memory O(samples)
• Only in Typical Set
• Great visualization tool !
• minus Approximate

First appeared in 70s, re-discovered by
Kitagawa, Isard Blake in computer
vision, Monte Carlo Localization in robotics
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Bayesian Filtering

• Two phases 1. Prediction Phase 2. Measurement
  Phase

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1. Prediction Phase
u
xt-1
xt
P(xt) ? P(xtxt-1,u) P(xt-1)
Motion Model
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2. Measurement Phase
z
xt
P(xtz) k P(zxt) P(xt)
Sensor Model
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1. Prediction Phase
u
P(xt ,u)
Motion Model
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2. Measurement Phase
P(zxt)
Sensor Model
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3. Resampling Step
O(N)
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Monte Carlo Localization
weighted Sk
Sk
Sk-1
Sk
Predict
Weight
Resample
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Particle Filter Tracking
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A Two-step View of the Particle Filter
Empirical predictive density Mixture Model
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Bayes Filter and Particle Filter
Recursive Bayes Filter Equation
Monte Carlo Approximation
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Conclusions

• Monte Carlo LocalizationPowerful yet
  efficientSignificantly less memory and CPUVery
  simple to implement

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Take Home Message

• Representing uncertainty using samples is
  powerful, fast, and simple !

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Questions
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1D Importance Sampling
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Monte Carlo Localization a 1D Example
Prior P(X)
Likelihood L(XZ)
Posterior P(XZ)
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Global Localization
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Global Localization (2)
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Global Localization (3)